Evaluation of MAX-DOAS aerosol retrievals by coincident ......tical resolution of the MAX-DOAS...

Atmos. Meas. Tech., 8, 2775–2788, 2015

www.atmos-meas-tech.net/8/2775/2015/

doi:10.5194/amt-8-2775-2015

© Author(s) 2015. CC Attribution 3.0 License.

Evaluation of MAX-DOAS aerosol retrievals by coincident

observations using CRDS, lidar, and sky radiometer in

Tsukuba, Japan

H. Irie1, T. Nakayama2, A. Shimizu3, A. Yamazaki4, T. Nagai4, A. Uchiyama4, Y. Zaizen4, S. Kagamitani2, and

Y. Matsumi2

1Center for Environmental Remote Sensing, Chiba University, 1–33 Yayoicho, Inage-ku, Chiba 263-8522, Japan2Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan3National Institute for Environmental Studies, 16–2 Onogawa, Tsukuba, Ibaraki 305-8506, Japan4Climate Research Department, Meteorological Research Institute, Japan Meteorological Agency, 1–1 Nagamine,

Tsukuba 305-0052, Japan

Correspondence to: H. Irie ([email protected])

Received: 21 January 2015 – Published in Atmos. Meas. Tech. Discuss.: 27 January 2015

Revised: 30 June 2015 – Accepted: 02 July 2015 – Published: 16 July 2015

Abstract. Coincident aerosol observations of multi-axis

differential optical absorption spectroscopy (MAX-DOAS),

cavity ring-down spectroscopy (CRDS), lidar, and sky ra-

diometer were conducted in Tsukuba, Japan, on 5–18 Oc-

tober 2010. MAX-DOAS aerosol retrieval (for aerosol ex-

tinction coefficient and aerosol optical depth at 476 nm) was

evaluated from the viewpoint of the need for a correction

factor for oxygen collision complexes (O4 or O2–O2) ab-

sorption. The present study strongly supports this need, as

systematic residuals at relatively high elevation angles (20

and 30◦) were evident in MAX-DOAS profile retrievals con-

ducted without the correction. However, adopting a single

number for the correction factor (fO4= 1.25) for all of the

elevation angles led to systematic overestimation of near-

surface aerosol extinction coefficients, as reported in the lit-

erature. To achieve agreement with all three observations, we

limited the set of elevation angles to ≤ 10◦ and adopted an

elevation-angle-dependent correction factor for practical pro-

file retrievals with scattered light observations by a ground-

based MAX-DOAS. With these modifications, we expect to

minimize the possible effects of temperature-dependent O4

absorption cross section and uncertainty in DOAS fit on an

aerosol profile retrieval, although more efforts are encour-

aged to quantitatively identify a physical explanation for the

need of a correction factor.

1 Introduction

Atmospheric aerosols play a critical role in controlling the

Earth’s climate and air quality (IPCC, 2013). Due to the

insufficient understanding of their complicated formation

mechanisms and effects, there is a growing need to under-

stand and measure their optical properties and precursors.

Under these circumstances, simultaneous measurements of

aerosols and their gaseous precursors, such as nitrogen diox-

ide (NO2) and sulfur dioxide (SO2), using the multi-axis

differential optical absorption spectroscopy (MAX-DOAS)

technique have been reported, with additional and signifi-

cant advantages of vertical profiling, simple setup, low power

consumption, and autonomous operation without absolute ra-

diometric calibration (Hönninger and Platt 2002; Hönninger

et al., 2004; Wittrock et al., 2004; Irie et al., 2008a, b, 2009,

2011). MAX-DOAS is an application of the well-established

DOAS technique, with which narrow band absorption fea-

tures are analyzed to selectively detect and quantify trace

gases by applying the Lambert–Beer law (Platt, 1994; Platt

and Stutz, 2008). In general, MAX-DOAS measures ultravi-

olet (UV)–visible spectra of scattered sunlight at several ele-

vation angles (α) between the horizon and zenith. Within the

boundary layer, for instance, observation at a low α yields

averaged information about trace gas concentrations over a

distance, which is in the same order of, or finer than, the

horizontal scale usually adopted by models and measured

Published by Copernicus Publications on behalf of the European Geosciences Union.

2776 H. Irie et al.: Evaluation of MAX-DOAS aerosol retrievals by coincident observations

by satellites but coarser than that of in situ observations.

Thereby, it is expected that MAX-DOAS plays an important

role in bridging different data sets with different spatial reso-

lutions (Irie et al., 2011). Thus, observations by MAX-DOAS

are highly unique and have great potential for realizing many

applied studies, including those on aerosols.

The number of MAX-DOAS instruments has grown con-

siderably in recent years (e.g., Roscoe et al., 2010; Piters et

al., 2012). The increasing use of MAX-DOAS instruments

for tropospheric observations, together with the diversity of

their designs and operation protocols, created the need for

formal comparison. For this purpose, the Cabauw Intercom-

parison Campaign of Nitrogen Dioxide measuring Instru-

ments (CINDI) was held at the Cabauw measurement sta-

tion (51.97◦ N, 4.93◦ E), the Netherlands, in June–July 2009.

During the CINDI campaign, besides the intercomparison for

NO2, near-surface aerosol extinction coefficients (AECs) re-

trieved from observations from four different MAX-DOAS

instruments were compared to those measured by the in situ

humidified nephelometer (Zieger et al., 2011). The compari-

son showed a tight correlation at a determination coefficient

R2 of 0.62–0.78, but the AECs from MAX-DOAS were a

factor of 1.5–3.4 larger than the in situ values. The system-

atic differences could have been caused by the limited ver-

tical resolution of the MAX-DOAS retrieval overestimating

the AECs in the lowest layer, as lofted aerosol layers were

present during the measurement period (Zieger et al., 2011;

Irie et al., 2011). However, sufficient evidence for their causal

link was not obtained. In relation to the discussion below, we

note here that a correction factor for the absorption of oxygen

collision complexes (O4 or O2–O2) was applied to all four

participating MAX-DOAS retrievals. This is based on obser-

vations by Wagner et al. (2009) and Clémer et al. (2010), who

indicated that retrieved O4 slant column densities (SCDs)

were systematically too high to match the model simulation

under near pure Rayleigh conditions, although a physical ex-

planation for applying the correction factor was unclear.

In the present study, coincident aerosol observations by

MAX-DOAS and those by cavity ring-down spectroscopy

(CRDS), lidar, and sky radiometer were conducted in

Tsukuba, Japan, on 5–18 October 2010. This occasion was

used to evaluate the MAX-DOAS aerosol retrievals of AECs

and aerosol optical depth (AOD) at 476 nm, particularly from

the viewpoint of the need for a correction factor for O4 ab-

sorption. Potential practical solutions to achieve agreement

of the MAX-DOAS observations with the three other obser-

vations are discussed.

2 Observations

2.1 MAX-DOAS

We installed our MAX-DOAS system at the Meteorological

Research Institute in Tsukuba, Japan (36.06◦ N, 140.13◦ E),

on 1 June 2010. Because the installed MAX-DOAS system

(PREDE, Co., Ltd) is basically the same as the one used for

the CINDI campaign (Irie et al., 2011) and for the MAX-

DOAS network of NO2 in Russia and Asia (MADRAS)

(Kanaya et al., 2014), only a brief description is given be-

low. A miniaturized UV–visible spectrometer (Ocean Optics,

Inc., USB4000) was used to record spectra between 223 and

557 nm. The temperature (T ) of the USB4000 spectrome-

ter was kept constant at 40.0± 0.1◦C to stabilize spectrome-

ter characteristics and to prevent possible dew condensation.

The spectral resolution (full width at half maximum) was

0.76 at 450 nm, as estimated by wavelength calibration us-

ing a high-resolution solar spectrum (Kurucz et al., 1984).

The integration time was kept constant throughout the day

at 150 ms. Spectra recorded at a fixed α for a 5 min interval

were averaged and analyzed. The line of sight was directed

to an azimuth angle of 316◦ (northwest). The field of view

was < 1◦. Spectra were recoded sequentially at six different

α of 3, 5, 10, 20, 30, and 90◦ using a movable mirror. This

sequence was repeated every 30 min.

Spectral analysis and subsequent profile retrieval were per-

formed using our new version of the Japanese MAX-DOAS

profile retrieval algorithm, version 2, which is the updated

version of the JM1 (Irie et al., 2011) used for CINDI. Be-

cause most parts are the same as the JM1, some detailed

descriptions have been omitted in this paper. The recoded

spectra were first analyzed by the so-called DOAS method

(Platt, 1994; Platt and Stutz, 2008), in which spectral fitting

is performed using the nonlinear least-squares method (Irie et

al., 2008a). The DOAS method retrieves the differential slant

column density (1SCD), defined as the difference between

the SCD along the path of sunlight for off-axis measure-

ments (α < 90◦) and the SCD for the reference measurement

(α = 90◦). Most of the absorption cross-section data used here

were the same as those used during the CINDI campaign

(Roscoe et al., 2010). For H2O, we used the 2009 edition of

the High-Resolution Transmission (HITRAN) database. For

O4, Hermans’ cross-section data at 296 K (Herman, 2011)

were used. Results obtained using the newly available O4

cross-section data of Thalman and Volkamer (2013) are dis-

cussed later.

The fitting window of 460–490 nm was analyzed for

aerosol retrievals at 476 nm. The wavelength corresponds to

the O4-cross-section-weighted mean wavelengths for the fit-

ting window. The fitting window was chosen to minimize the

wavelength dependence of the air mass factor (AMF) infor-

mation between representative wavelengths for O4 and NO2.

NO2 is the primary target gas for our MAX-DOAS obser-

vations (Irie et al., 2011). The retrieved quantity, 1SCD of

O4, is referred to as the 1SCD for quadratic O2 concentra-

tion (molecules2 cm−5) and therefore contains the equilib-

rium constant between O4 and two O2 molecules (Greenblatt

et al., 1990).

A set of O41SCD data obtained at all α was inverted

into the vertical profile of AECs at 476 nm. The nonlinear

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H. Irie et al.: Evaluation of MAX-DOAS aerosol retrievals by coincident observations 2777

inversion problem was solved by the Optimal Estimation

Method (Rodgers, 2000). To create a lookup table (LUT) of

the box-AMF vertical profile, which was required to calcu-

late O41SCD in the forward model, we used the radiative

transfer model JACOSPAR. The JACOSPAR was developed

based on its predecessor, the Monte Carlo Atmospheric Ra-

diative Transfer Simulator (MCARaTS) (Iwabuchi, 2006).

Box-AMF calculations by MCARaTS have been validated

by other radiative transfer models (Wagner et al., 2007). To

simulate a realistic atmosphere, we considered the surface

altitude at the measurement site (35 m a.s.l.) and the altitude

where the instrument was located (63 m a.s.l). In addition, in

the forward model, temporal variations in ambient tempera-

ture and pressure based on National Centers for Environmen-

tal Prediction surface data were considered.

In this inversion, components of the measurement vector

were set to O4 1SCD values at all α for a full α scanning

time of 30 min. Here, the O4 1SCD value derived from ob-

servations is denoted as O4 1SCD (obs) and that calculated

by the forward model is denoted as O4 1SCD (mdl). If the

inversion was perfectly finished, the O4 1SCD (mdl) should

be identical to O4 1SCD (obs) within the range correspond-

ing to measurement noises. However, if the systematic resid-

ual remained, these two quantities could be linked by the fol-

lowing:

O41SCD(mdl)× fO4= O41SCD(obs) (1)

or

fO4= O41SCD(obs)/O41SCD(mdl) , (2)

where fO4is the correction factor for O4 1SCD (mdl). This

factor was introduced to compensate for a possible discrep-

ancy between O4 1SCD (obs) and O4 1SCD (mdl). For in-

stance, a discrepancy could occur if there were a bias in O4

1SCD (mdl) due to a bias in O4 absorption cross-section

data. For the CINDI campaign, the adopted fO4values (and

their reciprocals, as described by Zieger et al., 2011) ranged

from 1.20 (0.83) to 1.33 (0.75), depending on the participat-

ing group (Zieger et al., 2011). Our JM1 algorithm adopted

1.25 (0.80), according to Clémer et al. (2010).

With the above setup, we retrieved four parameters, which

were used to construct the continuous AEC vertical profile.

The state vector (x) was then defined as

x = (AOD F1 F2 F3)T . (3)

The F values that range between 0 and 1 are the parameters

determining the shape of the vertical profile. Partial AOD

values for 0–1, 1–2, and 2–3 km are given as AOD×F1,

AOD×(1−F1)F2, and AOD×(1−F1)(1−F2)F3, respec-

tively, and the partial AOD above 3 km as AOD×(1−

F1)(1−F2)(1−F3). From the partial AOD above 3 km, we

determined a continuous AEC profile for the layer from 3

to 100 km assuming an AEC value at the top of the layer

Figure 1. Examples of aerosol extinction coefficient (AEC) profiles

retrieved from MAX-DOAS observations. These are derived from

four parameters of AOD, F1, F2, and F3, as described in detail in

the text. Parameters used are given in the plot.

(100 km) and an exponential profile shape. Similarly, we de-

termined continuous profiles for layers of 2–3, 1–2, and 0–

1 km. Examples of AEC vertical profiles parameterized in

this way are shown in Fig. 1. The a priori profile is shown

in red. When AOD was doubled, the AEC profile was sim-

ply scaled by a factor of 2 (Fig. 1). Increasing the F1 value,

for example, led to a greater fraction of AOD below 1 km,

resulting in a steep gradient of the AEC profile below 1 km.

When the F1 value decreased, the fraction of AOD below

1 km decreased. This resulted in a reduction of the gradient,

and the representation of an uplifted aerosol profile was pos-

sible (Fig. 1).

The a priori values (± error) used in the present study

were the same as those used for CINDI (Irie et al., 2011):

AOD= 0.21± 3.0, F1 = 0.60± 0.05, F2 = 0.80± 0.03, and

F3 = 0.80± 0.03. These yield an AEC of 0.13 km−1 as the

mean values for the 0–1 km layer. The corresponding error is

+2.22/−1.94 km−1, indicating the allowance for retrieving a

wide range of AECs. Non-diagonal elements of the a priori

covariance matrix were set to 0.

Output from the vertical profile retrieval was only avail-

able for retrieved AOD less than 3, which corresponds to the

largest value in the LUT. This excludes large optical depth

cases, most of which should be due to optically thick clouds.

Further data screening was made using the root-mean squares

of the residuals of the O4 1SCD values. Larger residuals

could occur when the above-mentioned method of construct-

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ing a vertical profile was too simple to represent the true pro-

file, particularly with a very steep vertical gradient of extinc-

tion due to clouds. In addition, rapid changes in optical depth

within the full α scanning time of 30 min could lead to larger

residuals. The threshold for these data screening was set to

10 % of the mean O4 1SCD (obs) in each 30 min interval.

2.2 CRDS

The CRDS instrument typically consists of two high-

reflectivity plano-concave mirrors set opposite one another.

A pulsed or continuous laser beam is coupled into the cavity

from one side, and performs multiple reflections inside the

cavity. A photodetector is placed at the other side of the cav-

ity and measures the exponential decay of the light intensity

transmitted through the cavity. By comparing the decay rates

measured in the presence and absence of aerosols, the AECs

can be determined.

At Tsukuba from 5 to 18 October 2010, the AECs at 355

and 532 nm were measured using a custom-built 2λ-CRDS

(Nakayama et al., 2010a, b). Ambient particles were sam-

pled through the PM10 inlet placed 54 m a.s.l. The decay

rates in the absence of aerosols were measured for 5 min ev-

ery 20 min by passing the particles through a high efficiency

particulate air filter (Pall). To determine the relative humid-

ity (RH) dependence of the AEC values, the AECs were

measured under high RH conditions (RH= 79.0± 0.6 %)

by passing the particles through a humidifier (Perma Pure

LLC, MD-110-24S-4) for 20 min every 60 min. The RH

and temperature in the cells were monitored using thermo-

hygrometers (Vaisala, HMT-337). The 60 min average expo-

nential dependence parameter of extinction on RH (γ ) was

calculated using a series of 20 min averages of AEC and RH

data as follows:

AECRH1(λ)/AECRH2

(λ)= [(100−RH1)/(100−RH2)]−γ ,

(4)

where AECRH1(λ) and AECRH2

(λ) are AEC values mea-

sured at RH1 and RH2, when aerosols were passed through

the humidifier. The AECs (AECamb(λ)) corresponding to the

ambient RH (RHamb), temperature, and pressure conditions

were then calculated using the γ values:

AECamb(λ)= (TcellPamb/TambPcell) (5)

×AECRHcell(λ)[(100−RHamb)/(100−RHcell)]

−γ ,

where Tcell and Tamb are temperatures, and Pcell and Pamb are

pressures in the cell and ambient air, respectively. The 60 min

averaged AECamb (476 nm) was estimated from the obtained

AECamb (355 nm) and AECamb (532 nm) using the extinc-

tion Ångström exponent between 355 and 532 nm and was

used for comparison with the MAX-DOAS data. The average

(± 1σ) relative uncertainty in the 60 min average AECamb

(476 nm) values was estimated to be 11(± 7)% from the un-

certainties in the AEC measurements at 355 and 532 nm and

in the corrections for RH and wavelength dependence.

During the CRDS measurements, aerosol scattering and

absorption coefficients (ASC and AAC, respectively) were

also measured using a 3λ nephelometer (TSI, model 3563,

450, 550, 700 nm) and a 3λ-particle soot absorption pho-

tometer (PSAP) (Radiance Research, 467, 530, 660 nm)

(Uchiyama et al., 2014). The nephelometer data were cor-

rected using the scattering Ångström-exponent-dependent

correction factors reported by Anderson and Ogren (1998).

The PSAP data were corrected based on the scheme reported

by Ogren (2010). These corrected data were used for com-

parison with the CRDS data after taking into account the dif-

ference in the RH, temperature, and pressure in the cells, as

well as the difference in wavelength. The AACs at 450 and

550 nm were estimated using the absorption Ångström expo-

nent between 462 and 526 nm and between 526 and 650 nm,

respectively, assuming that the AACs were independent of

RH. The AECs at 355 and 532 nm obtained by the CRDS

were corrected to the values corresponding to the RH in

the cell of nephelometer using the γ values. Then, the AEC

values at 450 and 550 nm were estimated using the extinc-

tion Ångström exponent and used for the comparison with

the nephelometer and PSAP data. The AECs estimated from

the CRDS data showed good agreement with the sum of the

ASCs measured by the TSI nephelometer and the AACs esti-

mated from PSAP data, with a slope of 1.01 (R2= 0.94) and

1.00 (R2= 0.93) at 450 and 550 nm, respectively.

2.3 Lidar

The lidar system operated was a compact Mie-scattering

system utilizing the fundamental and second harmonics of

a flashlamp-pumped neodymium-doped yttrium aluminum

garnet (Nd:YAG) laser (1064/532 nm) as the light source

(Shimizu et al., 2004). To solve the lidar equation, we as-

sumed a constant extinction-to-backscattering ratio (S) of 50

sr. The S ratio can vary by more than 30 % at Tsukuba, with

resulting errors in AEC due to the use of a fixed S occa-

sionally exceeding 30 % (Irie et al., 2008a). In quantitative

discussion of AEC values near the surface, the lidar aerosol

extinction data at 532 nm were converted into AEC value at

476 nm, which can be compared to the MAX-DOAS data, us-

ing coincident measurements of the Ångström exponent by

the CRDS. During the time period of this comparative ob-

servation, lidar data were sometimes affected by clouds. In

cases where clouds were present below 6 km, an AEC pro-

file was retrieved from data below the cloud base. This is not

the preference for the lidar data analysis and is potentially

the reason for the large uncertainty in derived AEC values

below clouds. Due to the lack of overlap between the laser

beam and the field of view of the telescope, the lowest height

of retrieved AECs was 120 m. Thereafter, assuming homo-

geneous mixing of aerosols below this altitude, we assumed



Figure 2. Vertical profiles of AEC values at 532 nm derived from

lidar observations. Black indicates the regions between the cloud

base and apparent cloud top. Gray corresponds to invisible regions

above clouds.

Figure 3. Mean vertical profiles of lidar AEC data at 532 nm for

5–18 October 2010. Profiles with the original vertical resolution

(30 m) and 1 km mean profiles are shown in black and red, respec-

tively. In this period, there are significant amounts of AECs even

above 2 km. Error bars represent 1σ standard deviations.

constant AEC values and their errors in the vertical direction

below 120 m.

2.4 Sky radiometer

A scanning sun–sky photometer called the sky radiometer

(Prede Co., Ltd, Tokyo, Japan) is the main instrument in the

ground-based observation network SKYNET (Nakajima et

al., 2007). A set of measurements of the direct solar irra-

diance and the solar radiance distributions was made with

Figure 4. Time series of AEC and AOD values at 476 nm on

5–18 October 2010. (Top) Near-surface AEC values from CRDS

and MAX-DOAS; (middle) AEC values for 0–1 km from lidar

and MAX-DOAS; (bottom) AOD values from sky radiometer and

MAX-DOAS are compared in respective plots. For the MAX-

DOAS retrieval, a fO4of 1.25 is assumed. Error bars for MAX-

DOAS represent uncertainty associated with the retrieval. Error bars

for CRDS represent the 1σ values estimated from the uncertainties

in the AEC measurements at 355 and 532 nm and in the corrections

for RH and wavelength dependence. Error bars for lidar represent

1σ standard deviations of original 30 m AEC values in the 0–1 km

layer.

the sky radiometer in 30 s to 2 min, depending on the so-

lar zenith angle. This was repeated every 10 min. The data

were analyzed to derive the aerosol optical properties (such

as AOD) at 340, 380, 400, 500, 675, 870, and 1020 nm us-

ing the SKYRAD.pack version 4.2 software package (Naka-

jima et al., 1996). The Ångström exponent was calculated

from these AOD values and was used to derive AOD values

at 476 nm. Aerosol optical properties retrieved from sky ra-

diometers/SKYNET have been used to investigate regional

and seasonal characteristics of aerosols for climate and envi-

ronmental studies and to validate satellite remote sensing re-

sults (Higurashi and Nakajima, 2002; Kim et al., 2005; Sohn

et al., 2007; Pandithurai et al., 2009; Campanelli et al., 2010;

Khatri et al., 2010; Takenaka et al., 2011). There are sev-

eral reports that the AOD values obtained have high accuracy

compared to those of the standard Langley method and those

from AERONET (Campanelli et al., 2007; Che et al., 2008).



Figure 5. Correlation plots (left) between near-surface AEC values from CRDS and MAX-DOAS, (center) between mean AEC values for

0–1 km from lidar and MAX-DOAS, and (right) between AOD values from sky radiometer and MAX-DOAS. In AEC plots, red symbols

show the averages of the MAX-DOAS AEC values for each 0.05 km−1 bin of CRDS or lidar data. The bin has been optimized considering

the number of bins and the number of data in each bin for all pairs of comparisons in this study. For the MAX-DOAS retrieval, a fO4of 1.25

is assumed.

3 Results and discussion

Temporal variations in vertical profiles of AECs at 532 nm

derived from lidar observations at Tsukuba for the period

of 5–18 October 2010 are shown in Fig. 2. This time pe-

riod can be characterized as a rather ordinary period with

moderate cloud occurrence. In addition, it can be seen that

most aerosols were located below an altitude of ∼ 2 km, and

significant, prolonged uplifted aerosols were not observed.

This differs from the situation during the CINDI campaign

period, when the uplifted aerosols could be attributed to

the discrepancy found in comparisons between MAX-DOAS

and the ground-based humidified nephelometer (Zieger et

al., 2011; Irie et al., 2011). In Fig. 3, the mean vertical

profile of lidar AEC data taken on 5–18 October is plot-

ted. Mean AECs above 3 km were about 0.03 km−1. Above

3 km, MAX-DOAS has a weak sensitivity to aerosols and

the JM2 vertical profile retrieval algorithm employs a param-

eterization that does not allow a significant number of AECs

(Fig. 1). This easily results in the underestimation of AECs

above 3 km and AOD.

In Figs. 4 and 5, MAX-DOAS aerosol data are compared

to CRDS AECs, lidar AECs, and sky radiometer AOD data.

The comparisons were made for a wavelength of 476 nm. In

the MAX-DOAS retrieval, a fO4of 1.25 was assumed, fol-

lowing the procedure taken in the CINDI campaign (Irie et

al., 2011). In general, temporal variation showed very sim-

ilar patterns (Fig. 4). A problem found in the comparisons

is that most of the MAX-DOAS AEC values at the near-

surface level show values larger than CRDS values (Fig. 5).

The AECs from MAX-DOAS were larger than CRDS values

by a factor of ∼ 1–4, which is comparable to that found by

Zieger et al. (2011) from similar comparisons during CINDI

(a factor of 1.5–3.4). The important point is that the system-

atic differences seen in the MAX-DOAS/CRDS comparisons

Figure 6. Same as Fig. 4, but a fO4of 1.00 is assumed in the MAX-

DOAS retrieval.

occurred even when uplifted aerosol layers were not often

present during the observation period of this study (Fig. 1).

This indicates that the occurrence of uplifted aerosols is not

the major reason causing significant differences.

As a physical reason for applying this correction fac-

tor is unclear, other comparisons were made assuming

fO4= 1.00 (i.e., no correction applied) for MAX-DOAS re-

trievals (Figs. 6 and 7). For comparisons made at the near

surface and at 0–1 km, the retrievals assuming fO4= 1.00



Figure 7. Same as Fig. 5, but a fO4of 1.00 is assumed in the MAX-DOAS retrieval.

Figure 8. Median values of residuals, O4 1SCD (obs) minus O4

1SCD (mdl), as a function of elevation angle. Values for retrievals

with fO4= 1.00 and fO4

= 1.25 are plotted with circles and squares,

respectively. Error bars represent 67 % ranges.

brought MAX-DOAS AEC values closer to CRDS and li-

dar data than those assuming fO4= 1.25. The mean differ-

ences of MAX-DOAS AEC values from CRDS and lidar data

were improved from +0.07± 0.09 and +0.03± 0.10 km−1

to +0.04± 0.08 and −0.02± 0.07 km−1, respectively. At

the same time, however, almost all of the MAX-DOAS

AOD values showed underestimation. In addition, simple lin-

ear regression analyses show rather poor correlations with

CRDS and lidar AEC data at R2 of ∼ 0.4 and 0.7, respec-

tively. Furthermore, the number of MAX-DOAS aerosol data

that survived after retrievals and data screening becomes

much smaller (N = 107) compared to that for retrievals with

fO4= 1.25 (N = 157). This is due to poor O4 1SCD fitting

results with relatively high residuals, particularly at high α,

as discussed in detail below.

To search for the cause, we focused on median val-

ues of residuals for profile retrievals, O4 1SCD (obs) mi-

nus O4 1SCD (mdl), as a function of α. As shown in

Fig. 8, we found that the residuals were very small (< 1042

molecules2 cm−5) at α ≤ 10◦. However, the residuals were

relatively large at α of 20 and 30◦. In particular, for retrievals

Figure 9. Individual profile retrieval residuals, O4 1SCD (obs) mi-

nus O4 1SCD (mdl), as a function of O4 1SCD (obs). Values for

retrievals with fO4= 1.00 are plotted. Values for α of 3, 5, 10, 20,

and 30◦ are shown in black, blue, green orange, and red, respec-

tively.

adopting fO4= 1.00, O4 1SCD (obs) values tended to be

systematically larger than O4 1SCD (mdl) values, indicat-

ing that the model values were underestimated. Clémer et

al. (2010) compared the measured and simulated O4 1SCDs

at α of 15 and 30◦ and found that values of the 1SCD (mdl)

values were systematically 25± 10 % smaller than the mea-

sured ones.

As found in MAX-DOAS/CRDS comparisons made ear-

lier, applying a single number for the correction factor

(fO4= 1.25) to all α yielded significant deviations in MAX-

DOAS AEC values from the CRDS data. In contrast, when

no correction factor was applied, agreement was improved.

These results gave us an idea that a different magnitude of

correction factor should be applied for different α, if a cor-

rection factor is needed.

To check if the correction factor is needed and to fur-

ther estimate empirically the required correction factor from



Figure 10. Relationships of 80, 90, and 95th percentiles of O4

1SCD (obs)/O4 1SCD (mdl) with α.

measurements, we analyzed the residuals of O4 1SCDs that

arose from individual retrievals for the case of fO4= 1.00. As

also seen from analysis of their median values (Fig. 8), the

individual residual was usually small at the lowest α (3◦)

(Fig. 9). While the lowest α is usually most important in

determining near-surface AEC, the MAX-DOAS AECs re-

trieved with a fO4= 1.00 agreed well with the CRDS val-

ues, as discussed above. This may suggest that no significant

correction factor is needed (i.e., the correction factor would

be close to unity) for the lowest α. In contrast, the residu-

als tended to be greater at higher α. In particular, as clearly

seen at α of 10, 20, and 30◦, the residual increases with an

increase in O4 1SCD (obs).

In principle, the O4 1SCD (mdl) has the upper limit

that corresponds to pure Rayleigh conditions. Under ambient

conditions with a certain amount of aerosols near the ground,

the upper limit for the O4 1SCD (mdl) values is approxi-

mated to correspond to conditions of very low aerosols above

the near-ground aerosol layer. When the O4 1SCD (obs) val-

ues are greater than the upper limit, their difference emerges

as the residual. This happened in our retrievals, as indicated

by the clear linear correlations between the residual and the

O4 1SCD (obs) for high α in Fig. 9.

To estimate the correction factor needed to explain the dis-

crepancy found in the fitting residuals, we investigated the

ratio (R) of O4 1SCDs (obs) to O4 1SCDs (mdl). An R ra-

tio close to unity means that the O4 1SCD (obs) is explained

by the O4 1SCD (mdl) with retrieved aerosol profiles. An

R ratio smaller than unity is potentially explained by artifi-

cially adding more aerosols in the retrieved aerosol profiles,

when AEC values are underestimated in the retrieved pro-

files. Similarly, an R ratio larger than unity can be explained

by artificially lowering AEC values.

Here, we make the hypothesis that a correction factor is

needed. If so, the correction factor fO4should correspond to

the largestR to compensate for as much residuals as possible.

Figure 11. Same as Fig. 4, but fO4is assumed to be a function of α

in the MAX-DOAS retrieval.

Considering that the estimate of R itself had uncertainty, the

largest R was estimated to be approximate to the 80th, 90th,

and 95th percentiles for each α. The largest R values esti-

mated in this way are plotted as a function of α in Fig. 10.

We found clear relationships between the largest R and α.

Interestingly, the regression lines pass over the point of R

at ∼ 1.25 at an α of 15◦, consistent with the estimate of the

correction factor by Clémer et al. (2010) for the α of 15◦.

This strongly supports the hypothesis that a correction factor

is needed, particularly for high α.

From these results, we derived the α-dependent correction

factor as

fO4= fO4

(α)= 1+α/60. (6)

Using this empirical equation, retrievals of AEC and AOD

were performed. Updated results for comparisons with

CRDS AECs, lidar AECs, and sky radiometer AOD data are

shown in Figs. 11 and 12. Compared to the results presented

earlier, reasonable agreements can be seen for the three com-

parisons with CRDS, lidar, and sky radiometer. For compar-

isons with CRDS and lidar AEC data, the values of deter-

mination coefficient R2 were as high as 0.96 and 0.89, re-

spectively. The mean differences of MAX-DOAS AEC val-

ues from CRDS and lidar data were as small as+0.01± 0.04

and −0.03± 0.05 km−1, respectively.



Figure 12. Same as Fig. 5, but fO4is assumed to be a function of α in the MAX-DOAS retrieval.

Table 1. Estimates of effective temperatures (Teff) for O4 absorp-

tion for an AOD (476 nm) of 0.1, a solar zenith angle of 45◦, and

a relative azimuth angle of 180◦. Surface temperature and pressure

are assumed to be 292 K and 986 hPa, respectively, according to

mean values at Tsukuba during the observation period.

Elevation angle (◦) 3 5 10 20 30

SCD-based Teff (K) 277 275 272 270 268

1SCD-based Teff (K) 283 279 276 274 271

However, this empirical equation for the correction factor

should be used with caution, unless the physical explanations

underpinning it are clarified. One potential reason for the

need for the correction factor is that O4 1SCD (obs) is less

accurate (more overestimated) at higher α. In fact, the na-

ture of molecular interactions in O4 is still under discussion

(e.g., Sneep et al., 2006). Recently, Thalman and Volkamer

(2013) performed laboratory measurements of the absorption

cross section of O4, σ (O4) at a pressure close to ambient

(825 hPa). Their σ (O4) data at 295 K agreed with Hermans

(2011) σ (O4) at 296 K within instrumental measurement er-

rors. The Hermans (2011) σ (O4) data were recommended

for MAX-DOAS aerosol retrievals during the CINDI cam-

paign and were also adopted in the present study. Thalman

and Volkamer (2013) found that the peak O4 cross sections

for the 477 nm absorption band (10−46 cm5 molec−2) were

temperature dependent and were 6.60, 6.91, and 7.67 at 293,

253, and 203 K, respectively. Values relative to 293 K are

1.00, 1.05, and 1.16, respectively. Thus, the peak O4 cross

section increases by a factor of 1.05 per 40 K reduction of

temperature from 293 to 253 K or ∼ 1.09± 0.025 per 44 K

reduction from 275 to 231 K (Thalman and Volkamer, 2013;

Spinei et al., 2015). The potential overestimation in 1SCD

(obs) due to the use of smaller O4 cross-section values at a

T higher than the actual one can be compensated for by the

same magnitude of fO4, according to Eq. (1). Based on at-

mospheric direct sun observations, there was no pressure de-

Figure 13. Same as Fig. 4, but a fO4= 1.00 is assumed in the MAX-

DOAS retrieval. α used in the retrieval was limited to ≤ 10◦.

pendence of the O4 cross section within their measurement

error of 3 % (Spinei et al., 2015).

In contrast, we estimated the 1SCD (SCD)-based effec-

tive temperature (Teff) for observations in the present study

(Table 1). For observations of this study, the mean surface

temperature was 292 K with a standard deviation of 7 K.

When the surface temperature varies by 7 K, the estimated

Teff also varies by 7 K under conditions given in the caption



Figure 14. Same as Fig. 5, but a fO4= 1.00 is assumed in the MAX-DOAS retrieval. α used in the retrieval was limited to ≤ 10◦.

of Table 1. However, Teff differences at different α angles

become much smaller. The Teff values for α of 3–30◦ ranged

from 283 (277) to 271 (268) K, yielding a reduction of Teff

by 12 K, when α increased from 3◦to 30◦. Using Eq. (6), the

rate is translated to an increase of fO4by a factor of 1.45

per 12 K reduction in temperature. Thus, the tendency for a

larger fO4to be needed at a colder Teff is consistent with that

deduced from experiments by Thalman and Volkamer (2013)

and Spinei et al. (2015), although the magnitude is different.

A similar discussion has been made in the study by Spinei et

al. (2015).

To investigate uncertainty in the retrieved1O4 SCD (obs),

additional DOAS fitting was performed. Adopting Thalman

and Volkamer (2013) O4 absorption cross-section data for

295 K increased 1O4 SCD (obs) by 2 % on average. Adopt-

ing the data for 203 K decreased1O4 SCD (obs) by 14 % on

average, which is comparable to the 16 % change in the peak

cross sections between 295 and 203 K. In this case, however,

residuals significantly increased. The combined use of the

two-temperature cross-section data of Thalman and Volka-

mer (2013) at 295 and 203 K resulted in a 2 % increase on

average. The impact of changing the degree of polynomial

and the degree of offset polynomial by± 1 was within± 3 %.

All of these tests were insufficient to quantitatively explain

Eq. (6). However, we note here that the results from these

tests do not support the accuracy of 1O4 SCD (obs). Sys-

tematic biases might occur particularly at high α due to a

relatively thin optical depth of O4.

The other potential cause of uncertainty is that the O4

1SCD (mdl) may be less accurate at higher α. However, cal-

culations of the box AMF by various radiative transfer mod-

els were validated by Wagner et al. (2009), and larger differ-

ences among them were seen at very low α. Therefore, this

is not likely a cause. In addition, there is the fact that direct

sunlight observations do not need a correction factor (Spinei

et al., 2015), suggesting that this issue is only for scattered

light observations. These discussions would help us identify

a physical explanation of the need for a correction factor in

the future.

Figure 15. Same as Fig. 4, but fO4is assumed to be a function of α

in the MAX-DOAS retrieval. α used in the retrieval has been limited

to ≤ 10◦.

Although the definitive physical explanations behind

Eq. (6) are unclear, it is clear that problems tend to occur

at relatively large α. Considering this, as a practical solution

we propose limiting the set of α to ≤ 10◦ to minimize the

above-mentioned potential impacts and to keep a sufficient

number of α for each profile retrieval. Under these condi-

tions, we tested two retrievals without (i.e., fO4= 1.00) or



Figure 16. Same as Fig. 5, but fO4is assumed to be a function of α in the MAX-DOAS retrieval. α used in the retrieval has been limited to

≤ 10◦.

with the correction factor (fO4= fO4

(α)). The respective re-

sults are shown in Figs. 13–14 and Figs. 15–16.

Although a set of α is limited to ≤ 10◦, we obtain overall

reasonable agreements similar to those seen for retrievals us-

ing all α. As the most significant difference between results

from retrievals with and without the correction factor, we can

see that almost all of the MAX-DOAS AOD values underes-

timated the sky radiometer AOD when the retrievals were

performed without any correction factor (Fig. 14). In addi-

tion, for comparisons with CRDS and lidar AECs, correla-

tions for retrievals adopting fO4(α) were likely more reason-

able (their respective R2 values of 0.84 and 0.80, and mean

differences of +0.02± 0.04 and −0.01± 0.08 km−1) than

those without a correction factor (R2 of 0.75 and 0.70, and

mean differences of +0.03 ± 0.05 and −0.03± 0.08 km−1).

Therefore, we propose limiting the set of α to ≤ 10◦and

adopting fO4(α) for practical profile retrievals. These are en-

couraged to be tested by other MAX-DOAS aerosol profile

retrieval algorithms.

Limiting the set of α to ≤ 10◦ lowers degrees of freedom

for signal (DOFS) but increases the number of available data

(Table 2). The former means that observations at α larger

than 10◦ can contribute to an increase in DOFS. Such obser-

vations at high α should be added when reasons for the large

1SCD fitting residuals found in Figs. 8 and 9 are quantita-

tively understood. The increased number of data again sup-

ports the tendency that fitting for α ≤ 10◦ is less subject to

the correction factor than that for α = 20◦ and 30◦. The in-

crease in the number of data is partly due to the fact that more

data under cloudy conditions became available. Excluding α

of 20 and 30◦ leads to the loss of sensitivity to extinction at

high altitudes, where clouds are usually more dominant than

aerosols. As a result, although the DOFS decreases, the ca-

pability for observing the boundary layer by MAX-DOAS is

expected to be enhanced.

Table 2. DOFS and the number of available data (N) for each case

of correction factor.

Correction factor and α range DOFS N

fO4= 1.25 and all α 2.5± 0.4 157

fO4= 1.00 and all α 2.2± 0.4 107

fO4= fO4

(α) and all α 2.4± 0.4 159

fO4= 1.00 and α ≤ 10◦ 2.0± 0.3 207

fO4= fO4

(α) and α ≤ 10◦ 2.1± 0.3 229

4 Conclusions

Coincident aerosol observations of MAX-DOAS with those

of CRDS, lidar, and sky radiometer at Tsukuba, Japan, on

5–18 October 2010 were used to evaluate the MAX-DOAS

aerosol retrieval from the viewpoint of the need for a correc-

tion factor for O4 absorption (fO4). After applying a fO4

of

1.25 to all of the elevation angles, the retrieved near-surface

AEC values were found to be significantly larger than those

from the surface observations by CRDS. These results are

consistent with those of Zieger et al. (2011), who analyzed

data from the CINDI campaign with similar correction fac-

tors. Without any correction factor, agreement was improved.

However, significant characterized residuals were left, par-

ticularly at relatively high elevation angles of 20 and 30◦.

From detailed analysis of residuals, we empirically deduced

an elevation-angle-dependent correction factor (Eq. 6) that

describes a larger correction factor at a higher elevation an-

gle. This worked well to improve agreements for all com-

parisons with CRDS, lidar, and sky radiometer. Equation (6)

accounts for the T dependence of O4 absorption cross sec-

tions measured by Thalman and Volkamer (2013) qualita-

tively but is insufficient quantitatively. Another potential rea-

son for the need of a correction factor is that O4 1SCDs

derived from DOAS fit might be less accurate at higher el-

evation angles. Although more investigation is encouraged

to quantitatively identify the cause, for minimizing such po-



tential effects we propose to limit the set of elevation angles

to ≤ 10◦and to adopt an elevation-angle-dependent correc-

tion factor for practical profile retrievals with scattered light

observations by the ground-based MAX-DOAS.

Acknowledgements. We thank PREDE Co., Ltd. for their technical

assistance in developing the MAX-DOAS instruments. The MAX-

DOAS observations at Tsukuba were supported by M. Nakazato.

This work was performed by the joint research program of the

Solar-Terrestrial Environment Laboratory, Nagoya University.

This study was supported by funds from KAKENHI (numbers

25220101 and 09894399), JST/CREST/EMS/TEEDDA, and

JAXA/ GCOM-C.

Edited by: A. Sayer

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